I have been using Ubuntu for a long time and one day after an update I faced a problem as:

Your profile could not be opened correctly.
Some features may be unavailable. Please check that the profile exists and you have permission to read and write its
contents.

After that I concentrated the error and found out that it was a minor error regarding file permission during some update. So I looked out for the solution. The error might be for the permission so I checked the profile file for Chromium browser. And finally got the solution.
[NOTE: If you want the old profile (i.e. you need all the extensions and settings used in old profile) then follow the following steps:
Open the terminal and type:

mv ~/.config/chromium/Default ~/.config/chromium/Backup
This will backup all the profile information. After this Run chromium browser.

Now type:

rm -rf ~/.config/chromium/Default
cp -R ~/.config/chromium/Backup ~/.config/chromium/Default
This will remove the newly created profile and replace the old one.

If that just doesn’t work or you don’t care the old profile, just do not follow the above step.

Hope